Browse > Article
http://dx.doi.org/10.14317/jami.2016.369

ON A HIGHER-ORDER RATIONAL DIFFERENCE EQUATION  

BELHANNACHE, FARIDA (Department of Mathematics and LMPA Laboratory, Mohamed Seddik Ben Yahia University)
TOUAFEK, NOURESSADAT (Department of Mathematics and LMAM Laboratory, Mohamed Seddik Ben Yahia University)
ABO-ZEID, RAAFAT (Department of Basic Science, The Valley Higher Institute for Engineering & Technology)
Publication Information
Journal of applied mathematics & informatics / v.34, no.5_6, 2016 , pp. 369-382 More about this Journal
Abstract
In this paper, we investigate the global behavior of the solutions of the difference equation $x_{n+1}=\frac{A+Bx_{n-2k-1}}{C+D\prod_{i=l}^{k}x_{n-2i}^{m_i}}$, n=0, 1, ..., with non-negative initial conditions, the parameters A, B are non-negative real numbers, C, D are positive real numbers, k, l are fixed non-negative integers such that l ≤ k, and mi, i=l, k are positive integers.
Keywords
Difference equation; global behavior; oscillatory; boundedness;
Citations & Related Records
연도 인용수 순위
  • Reference
1 R. Abo-Zeid, Global behavior of a higher order difference equation, Math. Solvaca 64 (2014), 931-940.
2 R. Abo-Zeid Global asymptotic stability of a higher order difference equation, Bull. Allahabad Math. Soc. 25 (2010), 341-351.
3 F. Belhannache, N. Touafek and R. Abo-Zeid, Dynamics of a third-order rational difference equation, Bull. Math. Soc. Sci. Math. Roum. Nouv. Ser. 59 (2016), 13-22.
4 F. Belhannache and N. Touafek, Dynamics of a third-order system of rational difference equations, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal., to appear.
5 E.M. Elabbasy and S.M. Elaissawy, Global behavior of a higher-order rational difference equation, Fasc. Math. 53 (2014), 39-52.
6 S. Elaydi, An Introduction to Difference Equations, 3rd ed, Springer, New York, 1999.
7 E.M. Elsayed, On the dynamics of a higher-order rational recursive sequence, Commun. Math. Anal. 12 (2012), 117-133.
8 E.M. Elsayed and T.F. Ibrahim, Solutions and periodicity of a rational recursive sequences of order five, Bull. Malays. Math. Sci. Soc. 38 (2015), 95-112.   DOI
9 E.M. Elsayed and T.F. Ibrahim, Periodicity and solutions for some systems of nonlinear rational difference equations, Hacet. J. Math. Stat. 44 (2015), 1361-1390.
10 E.M. Erdogan and C. Cinar, On the dynamics of the recursive sequence , Fasc. Math. 50 (2013), 59-66.
11 E.A. Grove and G. Ladas, Periodicities in Nonlinear Difference Equations, Advances in Discrete Mathematics and Applications, Volume 4, Chapman and Hall, CRS Press, 2005.
12 T.F. Ibrahim, Periodicity and Global Attractivity of Difference Equation of Higher Order, J. Comput. Anal. Appl. 16 (2014), 552-564.
13 T.F. Ibrahim and M.A. El-Moneam, Global stability of higher-order difference equation, Iran. J. Sci. Technol., Trans. A, Sci. in press.
14 V.L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993.
15 M.R.S. Kulenovic and G. Ladas, Dynamics of second order rational difference equations with open problems and conjectures, Chapman and Hall, CRC Press, 2001.
16 Q. Din, T.F. Ibrahim and K.A. Khan, Behavior of a competitive system of second-order difference equations, Sci. World J. 2014 (2014), Article ID 283982, 9 pages.
17 M. Shojaei, R. Saadati and H. Adbi, Stability and periodic character of a rational third order difference equation, Chaos Solitons and Fractals 39 (2009), 1203-1209.   DOI
18 S. Stevic, More on a rational recurrence relation, Appl. Math. E-Notes 4 (2004), 80-84.
19 N. Touafek, On a second order rational difference equation, Hacet. J. Math. Stat. 41 (2012), 867-874.